WASHINGTON (CNN) - A new national poll indicates that white and black Americans don't see eye to eye on last month's arrest of Harvard University professor Henry Louis Gates. The CNN/Opinion Research Corporation survey, released Tuesday, also suggests a racial divide over President Barack Obama's initial comments on the incident.

Fifty-four percent of those questioned in the poll say they don't think Cambridge, Massachusetts police office James Crowley acted stupidly when he arrested Gates at the professor's home after Crowley responded to a call that someone was breaking into the house. One in three say they think Crowley did act stupidly. But there's a major racial divide, with 59 percent of black respondents saying that Crowley acted stupidly compared to 29 percent of whites questioned.

Just over half of those polled feel that Gates acted stupidly, with three in 10 saying no. Broken down by race, 58 percent of whites say Gates acted stupidly, with African-Americans split on the question.

The arrest sparked a national discussion on the issue of racial profiling, which was amplified when President Obama weighed in on the matter. In a prime time news conference last month, Obama said "the Cambridge police acted stupidly in arresting somebody when there was already proof that they were in their own home."

Two days later, after criticism from police unions and after speaking with Crowley, Obama attempted to defuse the dustup. "Because this has been ratcheting up, and I obviously helped to contribute ratcheting it up, I want to make clear that in my choice of words, I think, I unfortunately gave an impression that I was maligning the Cambridge Police Department or Sgt. (James) Crowley specifically, and I could have calibrated those words differently. And I told this to Sgt. Crowley."

Fifty-four percent of those questioned say they think the president acted stupidly when the commented on the Gates arrest, with 32 percent disagreeing. But again, the poll indicates a racial divide, with more than six out of 10 whites feeling Obama acted stupidly but just one in four black respondents agreeing.

Six out of 10 approve of how the president's handled race relations, with nine out of ten African-Americans and 56 percent of whites approving.

Did Obama's initial comments damage his political standing?

"One-third of whites say that Obama's comments about this matter made them feel less favorable toward him, compared to only four percent of whites who feel more favorably toward Obama due to his comments," says CNN Polling Director Keating Holland. "But the majority of whites say that Obama's comments did not affect their views of him, and most whites approve of how Obama is handling race relations."

Fifty-two percent of Americans feel racism among police officers is common, with 44 percent saying it's rare. Whites are split on that question, with 86 percent of black respondents feeling racism among police offices is common.

Two-thirds of whites say that a white homeowner would have been arrested for the same behavior. Only a quarter of blacks agree.
"That difference may be due to life experiences - more than half of blacks say they have been treated unfairly by the police because of their race but only a handful of whites report the same kind of treatment," adds Holland.

The poll indicates that both blacks and whites believe that Friday's beer summit at the White House was a good idea. But was it a "teachable moment," as mentioned by the president?

"Not according to the public - blacks and whites agree that the whole controversy did not teach Americans a lesson that will lead to better race relations," says Holland.

The CNN/Opinion Research Corporation poll was conducted Friday through Monday, 7/31-8/3, with 1,136 adult Americans - including 226 African-Americans and 773 whites - questioned by telephone. The survey's sampling error is plus or minus 3 percentage points for the overall sample and plus or minus 6.5 percentage points for the breakdown by race.